The two men behind the proposed Islamic community center and mosque near ground zero are from different generations and distinct backgrounds — the imam, 61, grew up in England and Malaysia and immigrated to New York as a teenager; the real estate developer, 37, spent his early childhood in Brooklyn, then attended American schools overseas.

Each has his own public relations firm and behind-the-scenes advisers. They have individual — not always identical — visions for the project, which they occasionally call by different names: the imam still speaks of it as Cordoba House, a name laden with religious history, while the developer uses the less-charged Park51. And amid the swirling controversy about their shared mission, they sometimes give different answers to thorny questions.

When asked why they resist moving the center to defuse critics who call its location near ground zero insensitive, for example, Mr. Abdul Rauf said a move would anger Muslims overseas and endanger American troops. Mr. Gamal, though, has always based his adamant stance on a constitutional right to build what he wants, where he wants, declaring: “I’m an American, I’m a New Yorker. I don’t hold my faith responsible for 9/11.”

While some differences are only natural — an imam focused on religious activities planned for the center and a developer more likely to talk up the swimming pool — and could be complementary, they have sometimes undermined efforts to build support. Their loose coordination has caused public misunderstandings — sometimes dramatic ones, as when it was briefly believed that the imam had agreed to move the center in return for a fringe Florida pastor’s promise not to burn the Koran. And even some supporters say the two men’s differing priorities are making it harder, or at least more time consuming, to quell the controversy.

“They’re very different individuals and they have different interests in the project,” said Julie Menin, chairwoman of Community Board 1, which voted in favor of the project.

Sometimes, she said, “It seems that they’re on two separate pages.”

The two men met around 2006, when Mr. Gamal, who works downtown, began visiting Masjid al-Farah, the mosque in TriBeCa where Mr. Abdul Rauf has presided since the 1980s. Both came to Sufi Islam as adults, and they have a strong personal bond: Mr. Gamal said that hearing the imam’s Friday sermon for the first time was “a dose of spirituality I hadn’t had in the longest time.”

Soon after, he asked the imam to officiate at his wedding, and they began dreaming up the community center out of a shared concern about crowding at two existing mosques in Lower Manhattan.

Mr. Gamal describes himself as the man in charge of the planned center, 120,000 square feet in size, and the sole arbiter of its location. His real estate company owns and leases the properties where it is to be built, 45-51 Park Place.

Mr. Abdul Rauf describes himself as the center’s visionary. He tried to initiate a similar project in the 1990s but failed to raise the cash.

Both agree that the imam will run the mosque and its interfaith programs, though they are still working out what those programs should look like.

Further complicating the situation is the role of Daisy Khan, the imam’s wife, a chatty, sophisticated former interior designer with a public profile that complements but does not mirror her husband’s.

It was Ms. Khan who took a phone call last week from a Florida imam trying to dissuade the fringe pastor, Terry Jones, from burning the Koran on the ninth anniversary of 9/11, agreeing that “we” — it was never clear who — would meet with the pastor, who promptly declared on television that the imam had agreed to move the center.

In the initial confusion, not even Mr. Gamal was sure it was not true.

Ms. Khan, whose American Society for Muslim Advancement shares an office with her husband’s Cordoba Initiative near Columbia University, has often been involved in public relations about the project, particularly when Mr. Abdul Rauf was out of the country in August on a State Department trip to the Middle East. The couple shares a professional collaboration not unlike the one in the Clinton White House. But Mr. Gamal has recently let it be known that Ms. Khan has no official role in Park51.

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The most recent disconnect has come over a compromise being suggested, in which the community center would add worship space for Christians, Jews and others. Mr. Gamal at first appeared cool to the idea, while Mr. Abdul Rauf was quick to embrace it publicly, according to Ms. Menin, a supporter of the project who has suggested that such a move could attract a wider base of donors and support.

Ms. Menin said Mr. Gamal told her that existing plans for programs to bring together different religions were enough. The imam, who wrote in an Op-Ed essay in The New York Times on Sept. 7 that the center would include worship space for all faiths, seems more eager to compromise and “build more consensus,” Ms. Menin said.

Mr. Gamal’s spokesman, Larry Kopp, said Wednesday that Mr. Gamal had decided to include an ecumenical worship space, as long as it did not reduce the space available to Muslims, and that details would take time to work out.

On the larger question of the project’s proximity to the World Trade Center site, Kurt Tolksdorf, one of Mr. Abdul Rauf’s closest friends from college, said in a recent interview that he “would not be surprised” if the imam consented to changing the location, if only because the conflict was exhausting and saddening him. “He can oppose intolerance without building the mosque at that particular spot,” Mr. Tolksdorf said.

Mr. Gamal, meanwhile, has told supporters he feels more determined the shriller the opposition becomes.

Mr. Abdul Rauf, Mr. Gamal and others have insisted in interviews that they have no substantive disagreements about the project, just different roles and personalities.

“Sharif is a businessman and he owns the property; I’m an imam and a spiritual leader who has a vision,” Mr. Abdul Rauf said last week. “He is a very capable man, very deeply committed towards the goal, a contribution to our country, to our city, to our neighborhood.”

The imam, whose Cordoba Initiative has offices in a building packed with religious — mostly Christian — nonprofit groups and nicknamed the God Box, has spent much of his time since 9/11 networking with Jewish and Christian leaders, urging American Muslims to expand their civic roles at home while promoting moderation abroad. He has also been on something of a media campaign, appearing recently on “Larry King Live” and speaking on Monday at the Council on Foreign Relations.

Mr. Gamal, who became a broker and property manager with Soho Properties after an abortive college career and several brushes with the law, has largely retreated behind the scenes since the imam’s return to New York.

To Mr. Abdul Rauf, who always emphasizes the center’s interfaith agenda, its location near ground zero is essential to its message of healing 9/11’s wounds and promoting moderate Islam.

Mr. Gamal, who tends to emphasize plans for a “world-class” architectural design, swimming pool, cooking school, restaurant and performing arts center, said he had selected the site because it was near the crowded downtown mosques and inexpensive. Ground zero, he said, had “nothing to do with it.”

They initially agreed to call the center Cordoba House, for the Spanish city in which Muslims, Jews and Christians shared a scholarly golden age a thousand years ago, but Mr. Gamal changed the name to Park51 after some opponents said medieval Cordoba, which Muslims ruled from 711 until Christians conquered them in the 13th century, signified Muslim domination. The imam’s religious programs will still bear that name, and he seemed to use it to refer to the whole center in his essay in The Times.

The day after the essay appeared, Mr. Gamal issued a press release reminding people that the center’s name was Park51.

A version of this article appears in print on September 17, 2010, on Page A20 of the New York edition with the headline: One Project, One Faith, And Two Men Who Differ. Order Reprints|Today's Paper|Subscribe